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Magnetic miniband and magnetotransport property of a graphene superlattice

The eigen energy and the conductivity of a graphene sheet subject to a one-dimensional cosinusoidal potential and in the presence of a magnetic field are calculated. Such a graphene superlattice presents three distinct magnetic miniband structures as the magnetic field increases. They are, respectively, the triply degenerate Landau level spectrum, the nondegenerate minibands with finite dispersion and the same Landau level spectrum with the pristine graphene. The ratio of the magnetic length to the period of the potential function is the characteristic quantity to determine the electronic structure of the superlattice. Corresponding to these distinct electronic structures, the diagonal conductivity presents very strong anisotropy in the weak and moderate magnetic field cases. But the predominant magnetotransport orientation changes from the transverse to the longitudinal direction of the superlattice. More interestingly, in the weak magnetic field case, the superlattice exhibits half-integer quantum Hall effect, but with large jump between the Hall plateaux. Thus it is different from the one of the pristine graphene.